Category:Examples of Continuous Real Functions
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This category contains examples of Continuous Real Function.
Continuity at a Point
$f$ is continuous at $x$ if and only if the limit $\ds \lim_{y \mathop \to x} \map f y$ exists and:
- $\ds \lim_{y \mathop \to x} \map f y = \map f x$
Continuous Everywhere
Let $f: \R \to \R$ be a real function.
Then $f$ is everywhere continuous if and only if $f$ is continuous at every point in $\R$.
Continuity on a Subset of Domain
Let $A \subseteq \R$ be any subset of the real numbers.
Let $f: A \to \R$ be a real function.
Then $f$ is continuous on $A$ if and only if $f$ is continuous at every point of $A$.
Pages in category "Examples of Continuous Real Functions"
The following 8 pages are in this category, out of 8 total.
C
- Continuous Real Function on Closed Interval/Examples
- Continuous Real Function on Closed Interval/Examples/Reciprocal of 1 + e to the Reciprocal of x
- Continuous Real Function/Examples
- Continuous Real Function/Examples/Root of x at 1
- Continuous Real Function/Examples/Sine of Reciprocal of x
- Continuous Real Function/Examples/Sine of x over x with 1 at 0